In giving Telemachos confidence in the first four books of the Odyssey, is Athene simply using Telemachos for her own ends, or is she playing a sincere role in Telemachos’ life as a mentor?

Athena is not using Telemachus simply for her own ends.

Explanation:

Athena inspires Telemachus to embark on a journey that is the story of the first five books of the Odyssey. In the form of Mentes, a comrade Odysseus, Athena inspires Telemachus, giving him hope that his father is still alive and that the only way to find out the truth about his return is to go search for him personally. Again, in book two, Athena keeps the story going by making sure Telemachus continues on his journey to find his father. After giving a speech to the assembled people of Ithaca on how the suitors are ravaging his father’s wealth, Telemachus loses confidence in his ability to carry out Athena’s plan. However, Athena reassures him with her supportive words. Bolstered by Athena’s words Telemachus continues to prepare for his journey with newfound vigor.